Tevez keeps City's faint title hopes alive
Tevez struck on the stroke of half-time after Villa's Ciaran Clark gifted possession to Edin Dzeko in a dangerous area and the Bosnian set up his team-mate to beat goalkeeper Brad Guzan.
That was enough to move Roberto Mancini's side back to 12 points adrift of leaders Manchester United, but City are still a long-shot to regain the Premier League crown they won so dramatically last season.
Mancini conceded it would be hard to catch United, but he insisted his team would keep pushing Alex Ferguson's men right until the end of the season.
"We know it will be difficult but we will keep on trying. It was important to stay 12 points behind United and for us the championship is not over," Mancini said.
"We have to keep on winning and see. This is football, nothing is impossible.
"We are playing well. We had good chances and Aston Villa are a good team. It is strange that they are down there and for that reason I am happy with my team."
Villa remain in the relegation zone, with goal difference keeping Paul Lambert's struggling team below 17th placed Wigan in the battle for survival.